A popular method to solve the symmetric saddle point problem
(REF ), which we adopt in this work,
is to use a preconditioned MinRes solver [1]}
with the following block diagonal preconditioner
[2]}, [3]}:
\(\mathsf {P} =\left[\begin{tabular}{cc}\widehat{\mathsf {iA}}& 0 \\[.8ex]0 & \widehat{\mathsf {iS}}\end{tabular}\right]\) 
